Goal:
  
  A : Type
  B : Type
  R : A → B → Type
  R' : ∀ (a : A) (b : B), R a b → Type
  x : A
  y : B
  l : list A
  l' : list B
  r : R x y
  rs : All2 R l l'
  r0 : R' x y r
  a0 : All2_dep R' rs
  b0 : All2_dep R' (All2_cons r rs)
  b'' : list A
  b''0 : list B
  b' : All2 R b'' b''0
  b : All2_dep R' b'
  ============================
   ({|
      pr1 :=
        {|
          pr1 := x :: l; pr2 := {| pr1 := y :: l'; pr2 := All2_cons r rs |}
        |};
      pr2 := b0
    |} =
    {|
      pr1 := {| pr1 := b''; pr2 := {| pr1 := b''0; pr2 := b' |} |}; pr2 := b
    |}
    → ∀ (H := CoreTactics.block) (e : NoConfusionHom_All2_dep A B R R'
                                        (x :: l) (y :: l') 
                                        (All2_cons r rs)
                                        (All2_dep_cons r0 a0) b0),
        let H0 := CoreTactics.block in
        noConfusionHom_All2_dep_obligation_2 A B R R' 
          (x :: l) (y :: l') (All2_cons r rs) (All2_dep_cons r0 a0) b0
          (noConfusionHom_All2_dep_obligation_1 A B R R' 
             (x :: l) (y :: l') (All2_cons r rs) (All2_dep_cons r0 a0) b0 e) =
        e)


DEBUG:Going to execute:
cbv beta iota delta [TODO projection TODO projection] in id, id'
DEBUG LTAC Evaluated term: b
DEBUG LTAC Evaluated term: (All2_dep R' b')
Level 5: type of id
 has value 
(All2_dep R' b')


Goals:
  
  A : Type
  B : Type
  R : A → B → Type
  R' : ∀ (a : A) (b : B), R a b → Type
  b0 : All2_dep R' All2_nil
  b'' : list A
  b''0 : list B
  b' : All2 R b'' b''0
  b : All2_dep R' b'
  ============================
   ({|
      pr1 := {| pr1 := []; pr2 := {| pr1 := []; pr2 := All2_nil |} |};
      pr2 := b0
    |} =
    {|
      pr1 := {| pr1 := b''; pr2 := {| pr1 := b''0; pr2 := b' |} |}; pr2 := b
    |}
    → ∀ (H := CoreTactics.block) (e : NoConfusionHom_All2_dep A B R R' [] []
                                        All2_nil All2_dep_nil b0),
        let H0 := CoreTactics.block in
        noConfusionHom_All2_dep_obligation_2 A B R R' [] [] All2_nil
          All2_dep_nil b0
          (noConfusionHom_All2_dep_obligation_1 A B R R' [] [] All2_nil
             All2_dep_nil b0 e) = e)

  
  A : Type
  B : Type
  R : A → B → Type
  R' : ∀ (a : A) (b : B), R a b → Type
  x : A
  y : B
  l : list A
  l' : list B
  r : R x y
  rs : All2 R l l'
  r0 : R' x y r
  a0 : All2_dep R' rs
  b0 : All2_dep R' (All2_cons r rs)
  b'' : list A
  b''0 : list B
  b' : All2 R b'' b''0
  b : All2_dep R' b'
  ============================
   ({|
      pr1 :=
        {|
          pr1 := x :: l; pr2 := {| pr1 := y :: l'; pr2 := All2_cons r rs |}
        |};
      pr2 := b0
    |} =
    {|
      pr1 := {| pr1 := b''; pr2 := {| pr1 := b''0; pr2 := b' |} |}; pr2 := b
    |}
    → ∀ (H := CoreTactics.block) (e : NoConfusionHom_All2_dep A B R R'
                                        (x :: l) (y :: l') 
                                        (All2_cons r rs)
                                        (All2_dep_cons r0 a0) b0),
        let H0 := CoreTactics.block in
        noConfusionHom_All2_dep_obligation_2 A B R R' 
          (x :: l) (y :: l') (All2_cons r rs) (All2_dep_cons r0 a0) b0
          (noConfusionHom_All2_dep_obligation_1 A B R R' 
             (x :: l) (y :: l') (All2_cons r rs) (All2_dep_cons r0 a0) b0 e) =
        e)


DEBUG:Going to execute:
tac H

Goals:
  
  A : Type
  B : Type
  R : A → B → Type
  R' : ∀ (a : A) (b : B), R a b → Type
  b0 : All2_dep R' All2_nil
  b'' : list A
  b''0 : list B
  b' : All2 R b'' b''0
  b : All2_dep R' b'
  ============================
   ({|
      pr1 := {| pr1 := []; pr2 := {| pr1 := []; pr2 := All2_nil |} |};
      pr2 := b0
    |} =
    {|
      pr1 := {| pr1 := b''; pr2 := {| pr1 := b''0; pr2 := b' |} |}; pr2 := b
    |}
    → ∀ (H := CoreTactics.block) (e : NoConfusionHom_All2_dep A B R R' [] []
                                        All2_nil All2_dep_nil b0),
        let H0 := CoreTactics.block in
        noConfusionHom_All2_dep_obligation_2 A B R R' [] [] All2_nil
          All2_dep_nil b0
          (noConfusionHom_All2_dep_obligation_1 A B R R' [] [] All2_nil
             All2_dep_nil b0 e) = e)

  
  A : Type
  B : Type
  R : A → B → Type
  R' : ∀ (a : A) (b : B), R a b → Type
  x : A
  y : B
  l : list A
  l' : list B
  r : R x y
  rs : All2 R l l'
  r0 : R' x y r
  a0 : All2_dep R' rs
  b0 : All2_dep R' (All2_cons r rs)
  b'' : list A
  b''0 : list B
  b' : All2 R b'' b''0
  b : All2_dep R' b'
  ============================
   ({|
      pr1 :=
        {|
          pr1 := x :: l; pr2 := {| pr1 := y :: l'; pr2 := All2_cons r rs |}
        |};
      pr2 := b0
    |} =
    {|
      pr1 := {| pr1 := b''; pr2 := {| pr1 := b''0; pr2 := b' |} |}; pr2 := b
    |}
    → ∀ (H := CoreTactics.block) (e : NoConfusionHom_All2_dep A B R R'
                                        (x :: l) (y :: l') 
                                        (All2_cons r rs)
                                        (All2_dep_cons r0 a0) b0),
        let H0 := CoreTactics.block in
        noConfusionHom_All2_dep_obligation_2 A B R R' 
          (x :: l) (y :: l') (All2_cons r rs) (All2_dep_cons r0 a0) b0
          (noConfusionHom_All2_dep_obligation_1 A B R R' 
             (x :: l) (y :: l') (All2_cons r rs) (All2_dep_cons r0 a0) b0 e) =
        e)


DEBUG:Going to execute:
DepElim.do_case hyp

Goals:
  
  A : Type
  B : Type
  R : A → B → Type
  R' : ∀ (a : A) (b : B), R a b → Type
  b0 : All2_dep R' All2_nil
  b'' : list A
  b''0 : list B
  b' : All2 R b'' b''0
  b : All2_dep R' b'
  ============================
   ({|
      pr1 := {| pr1 := []; pr2 := {| pr1 := []; pr2 := All2_nil |} |};
      pr2 := b0
    |} =
    {|
      pr1 := {| pr1 := b''; pr2 := {| pr1 := b''0; pr2 := b' |} |}; pr2 := b
    |}
    → ∀ (H := CoreTactics.block) (e : NoConfusionHom_All2_dep A B R R' [] []
                                        All2_nil All2_dep_nil b0),
        let H0 := CoreTactics.block in
        noConfusionHom_All2_dep_obligation_2 A B R R' [] [] All2_nil
          All2_dep_nil b0
          (noConfusionHom_All2_dep_obligation_1 A B R R' [] [] All2_nil
             All2_dep_nil b0 e) = e)

  
  A : Type
  B : Type
  R : A → B → Type
  R' : ∀ (a : A) (b : B), R a b → Type
  x : A
  y : B
  l : list A
  l' : list B
  r : R x y
  rs : All2 R l l'
  r0 : R' x y r
  a0 : All2_dep R' rs
  b0 : All2_dep R' (All2_cons r rs)
  b'' : list A
  b''0 : list B
  b' : All2 R b'' b''0
  b : All2_dep R' b'
  ============================
   ({|
      pr1 :=
        {|
          pr1 := x :: l; pr2 := {| pr1 := y :: l'; pr2 := All2_cons r rs |}
        |};
      pr2 := b0
    |} =
    {|
      pr1 := {| pr1 := b''; pr2 := {| pr1 := b''0; pr2 := b' |} |}; pr2 := b
    |}
    → ∀ (H := CoreTactics.block) (e : NoConfusionHom_All2_dep A B R R'
                                        (x :: l) (y :: l') 
                                        (All2_cons r rs)
                                        (All2_dep_cons r0 a0) b0),
        let H0 := CoreTactics.block in
        noConfusionHom_All2_dep_obligation_2 A B R R' 
          (x :: l) (y :: l') (All2_cons r rs) (All2_dep_cons r0 a0) b0
          (noConfusionHom_All2_dep_obligation_1 A B R R' 
             (x :: l) (y :: l') (All2_cons r rs) (All2_dep_cons r0 a0) b0 e) =
        e)


DEBUG:Going to execute:
fun p =>
             DepElim.introduce p;
              DepElim.elim_case p || destruct p || (case p; clear p)

Goals:
  
  A : Type
  B : Type
  R : A → B → Type
  R' : ∀ (a : A) (b : B), R a b → Type
  b0 : All2_dep R' All2_nil
  b'' : list A
  b''0 : list B
  b' : All2 R b'' b''0
  b : All2_dep R' b'
  ============================
   ({|
      pr1 := {| pr1 := []; pr2 := {| pr1 := []; pr2 := All2_nil |} |};
      pr2 := b0
    |} =
    {|
      pr1 := {| pr1 := b''; pr2 := {| pr1 := b''0; pr2 := b' |} |}; pr2 := b
    |}
    → ∀ (H := CoreTactics.block) (e : NoConfusionHom_All2_dep A B R R' [] []
                                        All2_nil All2_dep_nil b0),
        let H0 := CoreTactics.block in
        noConfusionHom_All2_dep_obligation_2 A B R R' [] [] All2_nil
          All2_dep_nil b0
          (noConfusionHom_All2_dep_obligation_1 A B R R' [] [] All2_nil
             All2_dep_nil b0 e) = e)

  
  A : Type
  B : Type
  R : A → B → Type
  R' : ∀ (a : A) (b : B), R a b → Type
  x : A
  y : B
  l : list A
  l' : list B
  r : R x y
  rs : All2 R l l'
  r0 : R' x y r
  a0 : All2_dep R' rs
  b0 : All2_dep R' (All2_cons r rs)
  b'' : list A
  b''0 : list B
  b' : All2 R b'' b''0
  b : All2_dep R' b'
  ============================
   ({|
      pr1 :=
        {|
          pr1 := x :: l; pr2 := {| pr1 := y :: l'; pr2 := All2_cons r rs |}
        |};
      pr2 := b0
    |} =
    {|
      pr1 := {| pr1 := b''; pr2 := {| pr1 := b''0; pr2 := b' |} |}; pr2 := b
    |}
    → ∀ (H := CoreTactics.block) (e : NoConfusionHom_All2_dep A B R R'
                                        (x :: l) (y :: l') 
                                        (All2_cons r rs)
                                        (All2_dep_cons r0 a0) b0),
        let H0 := CoreTactics.block in
        noConfusionHom_All2_dep_obligation_2 A B R R' 
          (x :: l) (y :: l') (All2_cons r rs) (All2_dep_cons r0 a0) b0
          (noConfusionHom_All2_dep_obligation_1 A B R R' 
             (x :: l) (y :: l') (All2_cons r rs) (All2_dep_cons r0 a0) b0 e) =
        e)


DEBUG:Going to execute:
DepElim.introduce p;
            DepElim.elim_case p || destruct p || (case p; clear p)

Goals:
  
  A : Type
  B : Type
  R : A → B → Type
  R' : ∀ (a : A) (b : B), R a b → Type
  b0 : All2_dep R' All2_nil
  b'' : list A
  b''0 : list B
  b' : All2 R b'' b''0
  b : All2_dep R' b'
  ============================
   ({|
      pr1 := {| pr1 := []; pr2 := {| pr1 := []; pr2 := All2_nil |} |};
      pr2 := b0
    |} =
    {|
      pr1 := {| pr1 := b''; pr2 := {| pr1 := b''0; pr2 := b' |} |}; pr2 := b
    |}
    → ∀ (H := CoreTactics.block) (e : NoConfusionHom_All2_dep A B R R' [] []
                                        All2_nil All2_dep_nil b0),
        let H0 := CoreTactics.block in
        noConfusionHom_All2_dep_obligation_2 A B R R' [] [] All2_nil
          All2_dep_nil b0
          (noConfusionHom_All2_dep_obligation_1 A B R R' [] [] All2_nil
             All2_dep_nil b0 e) = e)

  
  A : Type
  B : Type
  R : A → B → Type
  R' : ∀ (a : A) (b : B), R a b → Type
  x : A
  y : B
  l : list A
  l' : list B
  r : R x y
  rs : All2 R l l'
  r0 : R' x y r
  a0 : All2_dep R' rs
  b0 : All2_dep R' (All2_cons r rs)
  b'' : list A
  b''0 : list B
  b' : All2 R b'' b''0
  b : All2_dep R' b'
  ============================
   ({|
      pr1 :=
        {|
          pr1 := x :: l; pr2 := {| pr1 := y :: l'; pr2 := All2_cons r rs |}
        |};
      pr2 := b0
    |} =
    {|
      pr1 := {| pr1 := b''; pr2 := {| pr1 := b''0; pr2 := b' |} |}; pr2 := b
    |}
    → ∀ (H := CoreTactics.block) (e : NoConfusionHom_All2_dep A B R R'
                                        (x :: l) (y :: l') 
                                        (All2_cons r rs)
                                        (All2_dep_cons r0 a0) b0),
        let H0 := CoreTactics.block in
        noConfusionHom_All2_dep_obligation_2 A B R R' 
          (x :: l) (y :: l') (All2_cons r rs) (All2_dep_cons r0 a0) b0
          (noConfusionHom_All2_dep_obligation_1 A B R R' 
             (x :: l) (y :: l') (All2_cons r rs) (All2_dep_cons r0 a0) b0 e) =
        e)


DEBUG:Going to execute:
DepElim.introduce p
Level 4: evaluation returns
DepElim.introduce p; DepElim.elim_case p || destruct p || (case p; clear p)
where
p := b
of type
constr of type tacvalue

Level 4: evaluation returns
DepElim.introduce p; DepElim.elim_case p || destruct p || (case p; clear p)
where
p := b
of type
constr of type tacvalue

Level 3: evaluation returns
DepElim.introduce p; DepElim.elim_case p || destruct p || (case p; clear p)
where
p := b
of type
constr of type tacvalue

Level 3: evaluation returns
DepElim.introduce p; DepElim.elim_case p || destruct p || (case p; clear p)
where
p := b
of type
constr of type tacvalue


Goals:
  
  A : Type
  B : Type
  R : A → B → Type
  R' : ∀ (a : A) (b : B), R a b → Type
  b0 : All2_dep R' All2_nil
  b'' : list A
  b''0 : list B
  b' : All2 R b'' b''0
  b : All2_dep R' b'
  ============================
   ({|
      pr1 := {| pr1 := []; pr2 := {| pr1 := []; pr2 := All2_nil |} |};
      pr2 := b0
    |} =
    {|
      pr1 := {| pr1 := b''; pr2 := {| pr1 := b''0; pr2 := b' |} |}; pr2 := b
    |}
    → ∀ (H := CoreTactics.block) (e : NoConfusionHom_All2_dep A B R R' [] []
                                        All2_nil All2_dep_nil b0),
        let H0 := CoreTactics.block in
        noConfusionHom_All2_dep_obligation_2 A B R R' [] [] All2_nil
          All2_dep_nil b0
          (noConfusionHom_All2_dep_obligation_1 A B R R' [] [] All2_nil
             All2_dep_nil b0 e) = e)

  
  A : Type
  B : Type
  R : A → B → Type
  R' : ∀ (a : A) (b : B), R a b → Type
  x : A
  y : B
  l : list A
  l' : list B
  r : R x y
  rs : All2 R l l'
  r0 : R' x y r
  a0 : All2_dep R' rs
  b0 : All2_dep R' (All2_cons r rs)
  b'' : list A
  b''0 : list B
  b' : All2 R b'' b''0
  b : All2_dep R' b'
  ============================
   ({|
      pr1 :=
        {|
          pr1 := x :: l; pr2 := {| pr1 := y :: l'; pr2 := All2_cons r rs |}
        |};
      pr2 := b0
    |} =
    {|
      pr1 := {| pr1 := b''; pr2 := {| pr1 := b''0; pr2 := b' |} |}; pr2 := b
    |}
    → ∀ (H := CoreTactics.block) (e : NoConfusionHom_All2_dep A B R R'
                                        (x :: l) (y :: l') 
                                        (All2_cons r rs)
                                        (All2_dep_cons r0 a0) b0),
        let H0 := CoreTactics.block in
        noConfusionHom_All2_dep_obligation_2 A B R R' 
          (x :: l) (y :: l') (All2_cons r rs) (All2_dep_cons r0 a0) b0
          (noConfusionHom_All2_dep_obligation_1 A B R R' 
             (x :: l) (y :: l') (All2_cons r rs) (All2_dep_cons r0 a0) b0 e) =
        e)


DEBUG:Going to execute:
fun p => first
             [ match p with
               | _ => generalize dependent p; intros p
               end
             | intros
             until
             p
             | intros
             until
             1
             | intros ]

Goals:
  
  A : Type
  B : Type
  R : A → B → Type
  R' : ∀ (a : A) (b : B), R a b → Type
  b0 : All2_dep R' All2_nil
  b'' : list A
  b''0 : list B
  b' : All2 R b'' b''0
  b : All2_dep R' b'
  ============================
   ({|
      pr1 := {| pr1 := []; pr2 := {| pr1 := []; pr2 := All2_nil |} |};
      pr2 := b0
    |} =
    {|
      pr1 := {| pr1 := b''; pr2 := {| pr1 := b''0; pr2 := b' |} |}; pr2 := b
    |}
    → ∀ (H := CoreTactics.block) (e : NoConfusionHom_All2_dep A B R R' [] []
                                        All2_nil All2_dep_nil b0),
        let H0 := CoreTactics.block in
        noConfusionHom_All2_dep_obligation_2 A B R R' [] [] All2_nil
          All2_dep_nil b0
          (noConfusionHom_All2_dep_obligation_1 A B R R' [] [] All2_nil
             All2_dep_nil b0 e) = e)

  
  A : Type
  B : Type
  R : A → B → Type
  R' : ∀ (a : A) (b : B), R a b → Type
  x : A
  y : B
  l : list A
  l' : list B
  r : R x y
  rs : All2 R l l'
  r0 : R' x y r
  a0 : All2_dep R' rs
  b0 : All2_dep R' (All2_cons r rs)
  b'' : list A
  b''0 : list B
  b' : All2 R b'' b''0
  b : All2_dep R' b'
  ============================
   ({|
      pr1 :=
        {|
          pr1 := x :: l; pr2 := {| pr1 := y :: l'; pr2 := All2_cons r rs |}
        |};
      pr2 := b0
    |} =
    {|
      pr1 := {| pr1 := b''; pr2 := {| pr1 := b''0; pr2 := b' |} |}; pr2 := b
    |}
    → ∀ (H := CoreTactics.block) (e : NoConfusionHom_All2_dep A B R R'
                                        (x :: l) (y :: l') 
                                        (All2_cons r rs)
                                        (All2_dep_cons r0 a0) b0),
        let H0 := CoreTactics.block in
        noConfusionHom_All2_dep_obligation_2 A B R R' 
          (x :: l) (y :: l') (All2_cons r rs) (All2_dep_cons r0 a0) b0
          (noConfusionHom_All2_dep_obligation_1 A B R R' 
             (x :: l) (y :: l') (All2_cons r rs) (All2_dep_cons r0 a0) b0 e) =
        e)


DEBUG:Going to execute:
first
[ match p with
  | _ => generalize dependent p; intros p
  end
| intros
until
p
| intros
until
1
| intros ]